Speaker: Dr. Guang Lin, Computational Mathematics Group, DOE Pacific Northwest National Laboratory
Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in modeling and simulation of complex systems. In this talk, a new formulation for quantifying uncertainty in the context of non-equilibrium plasma flow problem will be discussed with extensions to other fields of mechanics and to dynamical systems. An integrated simulation framework will be presented that quantifies both numerical and modeling errors in an effort to establish "error bars" in CFD. In particular, a review of high-order methods (Spectral Elements, Discontinuous Galerkin, and WENO) will be presented for deterministic flow problems. Subsequently, stochastic formulations based on Galerkin and collocation versions of the generalized Polynomial Chaos (gPC), and some stochastic sensitivity analysis techniques will be discussed in some detail.
Full DNS simulations are computational expensive. I will introduce a Galerkin-free, proper orthogonal decomposition-assisted computational methodology for numerical simulations of the long-term dynamics of the incompressible Navier-Stokes equations.
Several specific examples on DNS simulation of flow past cylinder, sensitivity analysis and uncertainty quantification of ion-electron two-fluid plasma flow will be presented to illustrate the main idea of our approach.